Abstract: | For weakly nonlinear hyperbolic equations of order n, n≥3, with constant coefficients in the linear part of the operator, we study a problem with nonlocal two-point conditions in
time and periodic conditions in the space variable. Generally speaking, the solvability of this problem is connected with
the problem of small denominators whose estimation from below is based on the application of the metric approach. For almost
all (with respect to the Lebesgue measure) coefficients of the equation and almost all parameters of the domain, we establish
conditions for the existence of a unique classical solution of the problem.
Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L’viv. Translated from Ukrainskii
Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 186–195, February, 1997. |